If a tree cast a 24 foot shadow at the same time that a 3 foot cast a 2 foot shadow find the height of the tree
To solve this problem, we can set up a proportion using the similar triangles formed by the tree and its shadow, as well as the shorter object and its shadow.
Let x represent the height of the tree.
According to the given information, the tree's shadow is 24 feet long while the shorter object's shadow is 2 feet long. Therefore, we have the proportion:
(x / 24) = (3 / 2)
To solve for x, we can cross multiply:
2x = 24 * 3
2x = 72
Finally, divide both sides by 2:
x = 72 / 2
x = 36
Therefore, the height of the tree is 36 feet.